Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacent and for every vertex ν ∈ V (G)\S, 1 ≤ |N(ν) ∩ S| ≤ 2, that is, every vertex ν ∈ V (G)\S is adjacent to at least one but not more than two vertices in S. In this paper, we discuss the existence of independent [1, 2]-sets in a family of trees called caterpillars
Settling Kahn's conjecture (2001), we prove the following upper bound on the number i(G) of independ...
The independent domination number of a graph G, denoted i(G), is the minimum cardinality of a maxima...
A graph G=(V, E) is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tre...
Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacen...
A [1, 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and ...
A subset S ⊆ V in a graph G = (V,E) is a [1, k]-set for a positive integer k if for every vertex v ∈...
AbstractA caterpillar graph is a tree in which the removal of all pendant vertices results in a chor...
A [1, 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and ...
Let G be a graph with vertex set and edge set V(G) and E(G), respectively. A subset X S V(G) is said...
A set S ⊆ V of the graph G = (V,E) is called a [1, 2]-set of G if any vertex which is not in S has a...
AbstractA subset S of vertices of a graph G is independent if no two vertices in S are adjacent. In ...
A spanning generalized caterpillar is a spanning tree in which all vertices of degree more than two ...
A subset S⊆V in a graph G=(V,E) is a [j,k]-set if, for every vertex vεV\-S, j≤|N(v)\∩S|≤k for non-...
Wilf found the maximum number of independent dominating sets of a tree using algebraic methods, whil...
Abstract. We consider the number of vertex independent sets i(G). In general, the problem of determi...
Settling Kahn's conjecture (2001), we prove the following upper bound on the number i(G) of independ...
The independent domination number of a graph G, denoted i(G), is the minimum cardinality of a maxima...
A graph G=(V, E) is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tre...
Given a graph G, a subset S ⊆ V (G) is an independent [1, 2]-set if no two vertices in S are adjacen...
A [1, 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and ...
A subset S ⊆ V in a graph G = (V,E) is a [1, k]-set for a positive integer k if for every vertex v ∈...
AbstractA caterpillar graph is a tree in which the removal of all pendant vertices results in a chor...
A [1, 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and ...
Let G be a graph with vertex set and edge set V(G) and E(G), respectively. A subset X S V(G) is said...
A set S ⊆ V of the graph G = (V,E) is called a [1, 2]-set of G if any vertex which is not in S has a...
AbstractA subset S of vertices of a graph G is independent if no two vertices in S are adjacent. In ...
A spanning generalized caterpillar is a spanning tree in which all vertices of degree more than two ...
A subset S⊆V in a graph G=(V,E) is a [j,k]-set if, for every vertex vεV\-S, j≤|N(v)\∩S|≤k for non-...
Wilf found the maximum number of independent dominating sets of a tree using algebraic methods, whil...
Abstract. We consider the number of vertex independent sets i(G). In general, the problem of determi...
Settling Kahn's conjecture (2001), we prove the following upper bound on the number i(G) of independ...
The independent domination number of a graph G, denoted i(G), is the minimum cardinality of a maxima...
A graph G=(V, E) is called a pairwise compatibility graph (PCG) if there exists an edge-weighted tre...
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